,M£-NRLF 


c  z  aba  sn 


GIFT  OF 


AN     INVESTIGATION 


OP    THE 


HYDRAULIC     JET     PUMP 


A  thesis  submitted  in  partial  satisfaction 
of  the  requirements  for  the  degree  of 

MASTER  OP  SCIENCE 
at  the  University  of  California 


HOWARD  HAMILTON  BLISS 


Berkeley,   California,  April,   1913 


ff  a  Y  K 


Object  -  Description     of     Pump 

*!'*'•*••**•'  * 

It  was  the  purpose  of  the  work  herein  described  to 
study  the  operation  of  the  hydraulic  jet  pump  in  the  laboratory  of 
the  University  of  California.   The  investigation  included  finding 
the  loss  coefficients  in  each  part  of  the  pump,  testing  various  ar- 
rangements of  the  parts  for  efficiency,  and  studying  the  rate  at 
which  tha  parallel  jets  of  water  unite  to  acquire  a  common  velocity. 
An  attempt  was  made  to  test  experimentally  the  accuracy  of  a  theore- 
tical expression  for  the  impact  losses,  which  are  very  large  in  this 
kind  of  apparatus.  Finally,  certain  relations  were  analytically  de- 
veloped for  the  operation  of  the  device,  and  tests  and  calculations 
made  to  check  them  practically. 

This  jet  pump  has  two  concentric  cylindrical  cham- 
bers, the  inner  one  for  the  high  pressure  working  water  and  the  other 
for  the  low  pressure  water  to  be  lifted.  The  liquid  emerges  from 
these  compartments  through  concentric  nozzles,  the  low  pressure  water 
coming  through  the  annular  orifice  surrounding  the  other.  Because  of 
the  difference  in  head,  the  jet  in  the  center  has  a  higher  velocity, 
and  the  operation  of  the  pump  depends  upon  the  communication  of  this 
to  the  surrounding  water.  The  streams  mingle  in  the  mixing  chamber 
and  then  enter  the  diffuser,  where  the  kinetic  energy  is  largely 
converted  into  pressure. 

The  pump  tested  has  .a  number  of  mixing  chambers 

of  different  lengths,  any  one  of  which  can  be  set  between  the  nozzles 
and  the  diffuser.  They  are  all  cylindrical,  the  diameter  at  every 
point  being  five-eighths  inch,  which  is  also  the  diameter  of  the  ou- 
ter nozzle  and  of  the  throat  of  the  diffuser. 

o  4  rr  Kf\  4 


:"  !  o    ,  '  "•  -  • 


So 


. 


i* 


Nomenclature  -  Efficiency  tests 

In  making  the  tests  described  below,  the  low  pres- 
sure water  was  taken  from  a  storage  tank  by  a  centrifugal  pump  which 
delivered  it  to  a  stand  pipe,  whence  it  flowed  through  piping  and 
valves  to  the  jet  pump.  The  rest  came  from  the  tank  through  a  Quimby 
screw  pump  and  a  water  meter.  The  delivery  water  was  usually  weighed 
and  sent  into  the  storage  tank.  For  some  of  the  tests,  however,  it 
was  allowed  to  issue  into  the  open  air  and  was  diverted  downward  into 
the  weir  box  on  which  the  jet  pump  was  located.  The  other  apparatus 
used  consisted  of  two  pressure  gauges,  a  mercery  manometer,  a  water 
manometer,  a  watch,  and  a  Pitot  tube  built  especially  for  this  pump. 

It  will  be  necessary  in  this  report  to  express  by 

formulas  the  relations  of  various  quantities  measured  and  computed. 
After  trying  in  vain  to  make  satisfactory  use  of  a  system  of  nomen- 
clature with  numerical  subscripts,  I  have  developed  a  system  using 
the  letters  B,   e,  r,  j_,   m,   t_,  d,   and  f  as  subscripts.  A 
glance  at  sketch  No.  1  vill  make  clear  their  use.   Thus  Qs  signifies 
the  cubic  feet  of  suction  water  per  second,  vs  its  velocity,  and  hg 
its  pressure  head  (measured  in  feet  of  -ater  above  an  absolute  vacuum), 
Subscript  _e  indicates  the  high  pressure  water  entering  the  pump,  r 
signifies  the  annular  nozzle  stream,  j_  the  inner  jet,  m  the  mixing 
chamber,  £  the  throat  of  the  diffuser,  d  the  diffuser,  and  f_  the  final 
condition  as  the  water  leaves  the  apparatus.  The  letter  a  indicates 
area  of  cross  section  in  square  feet,  and  "|  is  the  loss  coefficient. 

EFFICIENCY   TESTS 

On  account  of  the  high  speed  at  which  the  water 
passes  through  the  mixing  chamber,  it  was  expected  that  a  considerable 

loss  of  energy  would  occur,  due  to  friction  there.  Hence  a  variation 


:jSV  ni 


sr 


a  of     testing      efficiency 

in  the  length  of  the  chamber  would  change  the  efficiency,    as  this 
loss  would  increase  with  increasing  length.   However,    since  the   entire 
operation  of  the  pump  depends  upon  the  imparting  of  the  kinetic   ener- 
gy of   the  working  water  to  the  surrounding  stream,    too  short  a  chamber 
would  also  destroy  the  efficiency. 

These  assumptions  were  abundantly  justified  by  two 

series   of  tests  with  varying   lengths.    In  the  first   series  the  working 
water     was  always  admitted  to  the  pump  at   70  Ibs.  per  D"  above  atmos- 
phere and  the  suction  \vater  entered  at   atmospheric  pressure.   In  the 
second  series  the  pressures  were  39.4#/D"  and  atmospheric.  With  each 
mixing  chamber  twelve  or  more  runs  were  made  with  different  delivery 
pressures.   For  each  run  the  data  taken  consisted  of  the  delivery 
pressure,    the  weight   of   vater  delivered,    the  cubic  feet   of  high  pres- 
sure water  used,    and  the  duration  of  the  run.   All  pressures  were  kept 
constant  and  verified  several  times  during   each  test.   The  gauges  were 
calibrated  practically  every  day  and  four  tests   of  the  water  meter 
at  different  times   showed  that   its  readings  were  reliable  within  the 
limit    of  errors   of   observation. 

The  efficiency,   n  ,    is  computed  as  foot  Ibs.    of 
work  done  on  the  water  lifted  +  foot  Ibs.    of  energy  lost  by  the 
working  fluid.   Letting  t  represent  the  seconds,  n    =     +  S8fhf  IhR1 

V  w      V^_  \^o     "~  11^  / 

(t   Of  -  tQ0)pf 

tt  Q  np"  -  "p£ )  »  ***re  P_  indicates  gauge  pressures,  pg  being  0. 

On  curve  sheets  Nos.  6  to  10  inclusive  will  be 

found  plotted  the  results  of  these  tests  upon  chambers  varying  in 
length  from  0  to  6  inches.  Under  otherwise  constant  conditions  the 
efficiency  varies  with  varying  delivery  pressure,  reaching  a  maxi- 
mum when  this  is  about  34  %  of  the  high  pressure  (by  gauge).  The 


!to 


*i 


•• 


Results     of     efficiency     tests  ^ 

greatest   efficiency  with  zero  mixing  chamber  is  22,7  $>.   Each  succeeding 
longer  chamber  s1  owg  better  operation  until  the   length  becomes  13/8 
inches.   For  this  and  those   of   lengths  2",    2  1/2"  and  3"  the  maxima  are 
•almost   equal  within  the  limit   of  probable  error  at  about  31  $>.   Beyond 
three   inches  the  efficiency  falls     gradually  until  it  reaches  25  % 
for   the  six  inch  chamber.     This  is  shown  graphically  on  curve  sheet 
No. 10  ,   which  is  plotted  from  the  previous  curves. 

r 

Tabulated  below  will  be  found  the  data  of  these 
runs.  In  most  cases  more  runs  were  made  than  recorded  here,  but 
the  more  inefficient  ones  v/ere  omitted.  It  will  be  noticed  that  the 
time  is  recorded,  though  not  use*  in  computing  efficiency.  It  was 
measured  necessarily  while  making  the  runs  -  as  most  of  the  time  I 
had  no  assistant  and  had  to  read  the  water  meter  a  definite  number 
of  seconds  after  attending  to  the  weighing  -  and  is  inserted  here 
with  the  idea  that  it  may  be  useful  for  later  study  from  this  data. 
The  series  on  the  two  inch  chamber  was  run  last  and  most  carefully, 
the  time  being  extended  more  than  ordinarily  to  decrease  the  effect 
of  errors  in  reading  the  meter. 

Mixing  chamber  0"  long. 

IPe  =,  39. 4# /D'  pe  =  70.07f/n« 

Pf   t  QQ  t  Q3    H      t        pf   t  Qe  t  Qs    >v     t 


17.5 

7.2 

•0.8 

2.9 

131 

17.3 

9.9 

6.1 

20.2 

126 

15.7 

6.7 

1.3 

12.9 

120 

19.2 

9.0 

5.4 

22.7 

116 

14.1 

6.3 

1.7 

15.0 

111 

21.2 

7.8 

3.4 

13.9 

100 

12.4 

5.7 

2.3 

18.6 

99 

53.3 

6.0 

2.0 

1617 

78 

10.8 

7.0 

4.2 

21.8 

120 

25.4 

8.9 

2.3 

14.7 

118 

8.9 

5.5 

4.1 

21.8 

89 

28.3 

6.8 

1.2 

12.0 

92 

.'>  r 


no  yl.l  :cs  nuwsfr.  ai  ;  .  >rf:   rfoni  xia  &: 

^•otvsaq  etf*  ffloa?  6e**of,i  t.Jt  ietrTw    ,  01. o^ 


oa  eesj0o 
.te  6TOT-  s&xo  tfrtoioi 


on 


Efficiency  testa  taoulated 


Mixing  chamber  1"  long. 
=  39.4  #/r»  £„  =  70. 0#  /D' 


Pf 

t 

t 

n 

t 

Pf 
19.7 

23.4 
25.2 
27.1 
28.9 
31.1 

t 
7. 
7. 
5. 
9. 
9. 
9, 

fc 

6 
6 
2 
7 
3 

4.18 
3.6 
2.4 
3.6 
3.1 
1.9 

22.6 
23.8 
24.2 
24.7 
23.5 
16.4 

Mixing 

chamber  13/8   " 

long 

18.8 

10.5 

2. 

3 

20.0 

190 

21.3 

7. 

0 

4.2 

26.2 

17.5 

6. 

1 

1. 

9 

24.9 

108 

23.3 

12. 

1 

7.2 

29.7 

15.8 

5* 

c 

. 

4 

23;  7 

98 

35.4 

7. 

4 

3.8 

29.2 

13.5 

7. 

9 

4. 

9 

32.4 

138 

27.5 

5. 

3 

2.7 

33.0 

11.6 

6. 

7 

4. 

5 

28.0 

112 

29.5 

11. 

5 

4.5 

28.5 

10.0 

5. 

7 

3. 

9 

23.2 

90 

31.5 

8. 

4 

2.8 

27.3 

Mixing 

chamber     2 

"    long 

9.3 

9. 

8 

7. 

8 

24.7 

174 

32.8 

18. 

3 

2.5 

12.0 

. 

9. 

7 

6. 

3 

29.1 

178 

30.4 

15. 

0 

4.2 

21.5 

15.0 

id). 

65 

5. 

35 

30.9 

203 

27.1 

11. 

1 

4.9 

27.9 

17,5 

13 

.9 

3. 

7 

21.3 

268 

24.9 

13. 

7 

7.1 

28.6 

19.1 

13 

.2 

1. 

4 

8.2 

318 

22.6 

11. 

9 

7.3 

29.3 

20.1 

9. 

4 

6.6 

28.3 

17.7 

9. 

7 

6.3 

22.0 

Mixing 

chamber  2 

1/2    » 

long 

8.9 

6. 

2 

5. 

0 

23.5 

101 

32.5 

6. 

3 

1.7 

23.4 

11.0 

5. 

4 

4. 

2 

30.0 

89 

30.6 

5. 

9 

2.1 

27.6 

13.5 

4. 

9 

3. 

1 

29.4 

81 

28.5 

6. 

7 

2.9 

29.7 

14.6 

5. 

3 

2. 

7 

30.0 

90 

2  5..  5 

6. 

3 

3.3 

30.0 

15.9 

10. 

1 

4. 

3 

28.8 

174 

23.5 

7. 

1 

4.1 

29.2 

17.5 

17. 

9 

6. 

1 

27.2 

316 

21.3 

5. 

0 

3.0 

26,3 

Mixing 

chamber  3" 

long 

18.4 

6. 

8 

1. 

2 

15.4 

119 

32.4 

6. 

3 

1.7 

23.3 

16.8 

5. 

8 

2. 

2 

23.2 

102 

30.6 

5. 

9 

2.1 

37.6 

14,9 

5. 

3 

2. 

8 

32.8 

89 

23.7 

5. 

7 

2.3 

28.0 

13.3 

4. 

9 

3. 

1 

33.2 

79 

26.5 

6. 

3 

3.3 

31.9 

11/7 

5. 

5 

4. 

1 

31.5 

90 

24.4 

7. 

3 

3.9 

28.6 

10.8 

4. 

7 

3. 

3 

26.5 

75 

21.6 

7. 

4 

3.8 

23.0 

J.:ixing 

chamber  4" 

long 

10.6 

4. 

8 

3. 

2 

22.7 

77 

32.3 

6. 

2 

1.8 

24.8 

12.4 

5. 

7 

3. 

9 

30.9 

93 

30.0 

5. 

7 

2.3 

30.2 

14.1 

5. 

3 

2. 

7 

28.3 

85 

27.6 

5. 

4 

2.6 

31.4 

15.8 

5. 

7 

2, 

3 

27.2 

96 

25.4 

5. 

3 

2.7 

29.0 

17.4 

6. 

2 

1. 

8 

23.0 

106 

23.2 

6. 

6 

3.0 

22.5 

18,4 

5. 

4 

1. 

0 

16.2 

103 

20.5 

6. 

4 

3.2 

20.7 

95 

155 

97 

73 

153 

114 


273 
223 
163 
197 
170 
134 
134 

86 
77 
88 
82 
91 
64 


76 
80 
75 
82 
92 
92 


84 
76 
72 
67 
80 
80 


" 


. 


Traverses     of     mingling 
Mixing 

streams 
chamber 

5"   long 

6 

Pe  = 

=  39.4 

#/[ 

pfi  = 

70.0 

#/  d" 

Pf 

20.2 

6.46 

t   Qa 
0.0 

0.0 

t 
105 

Pf 
2176 

t  Qe 

6.3 

t   Qs 
3.3 

23.4 

t 
81 

18.3 

4.0 

0.8 

17.3 

74 

24.2 

7.4 

3.8 

27.1 

94 

1616 

5.9 

2.1 

25.9 

102 

26.4 

5.5 

2.5 

27.6 

71 

14.7 

8.5 

4.3 

30.1 

146 

28.6 

6.9 

2.7 

29.1 

92 

12.9 

4.9 

S.I 

30.8 

84 

30.5 

6.0 

2.0 

25.8 

82 

10.7 

5.8 

3.8 

24.4 

93 

31.7 

7.7 

1.9 

20.4 

105 

Mixing 

chamber 

6"   long. 

•/ 

9.6 

6.0 

3.5 

18.8 

107 

21.5 

5.4 

2.6 

21.3 

72 

11.7 

5.1 

2.9 

24.0 

93 

24.4 

5.5 

2.5 

23.6 

76 

13.7 

S.7 

2.3 

21.5 

99 

28.2 

5.8 

2.2 

25.6 

82 

15.7 

5.8 

2.2 

25.1 

107 

31.1 

6.4 

1.6 

20.0 

90 

17.7 

7.8 

1.7 

17.8 

142 

34.0 

7.5 

0.5 

6.3 

104 

19.6 

7.3 

0.7 

9.5 

140 

TRAVERSES     OF     MINGLING     STREAMS 

In  order  to  study  the  manner  in  which  the  inner  and 
outer    jets  combine,    I  made  a   series  of  traverses  with  a  pitot   tube 
at   different   distances  from  the  nozzles.      The  first  was  very  close, 
within     about   1/32   of  an  inch  of  the   tips.  For  the   other  traverses 
I  attached  mixing  chambers   of   lengths  varying  from  one  to  six  inches 
and  tested  the  spped  at  the  open  end.   In  every  case  the  water  spurted 
into  the  open  air  and  was  defledted  downward  into  the  weir  box. 
Pressures  behind  the  nozzles  were  kept  constant  at   50#/D"  and  9.0 
#/D"  for  all  of  these  tests.    The  Pitot   tube  was  moved  across   in 
steps  averaging    ,o2"  each    (less  where  the  speed  was   varying),    and 
the  pressure  witlin  it  read  on  a  gauge  at   each  step. 

Taking  the  constant   of  the  tube  as    .99,   a  value 
determined  by  Professor  LeConte,    the  velocity  at  any  point   is 
.99  V^g  h  ,   where  h  is  the  head  in  feet    of  water  corresponding  to     p    , 
gauge   reading.    Hence  v  =  .99  ^64.4  x  p  x   144/62.4     =  12.07J  p 
The  velocities  are  plotted  on  curve  sheets  Nos.  1      to    3     inc. 


aea-rov 


p 


t  lo  lia 


Results  of  mingling  stream  traverses 

'It  will  be  seen  by  reference  to  the  curves  that  the 
streams  act  upon  each  other  to  a  considerable  extent  within  one  inch 
of  the  nozzles,  the  inner  part  of  the  annular  jet  gaining  speed  lost 
by  the  outer  part  of  the  other.  Friction  against  the  mixing  tube  is 
seen  to  decrease  the  peripheral  speed  of  the  annular  stream. 

With  each  increase  in  length  these  effects  become 
more  marked,  except  that  the  higher  speed  is  gradually  communica- 
ted clear  to  the  periphery  of  the  outer  jet  and  counteracts  the 
friction  on  the  walls.  The  rubbing  velocity,  which  commenced  at 
25  ft.  per  second,  drops  to  about  21  within  the  first  1  3/8  "  and 
then  rises  gradually  until  it  reaches  45  ft.  per  second  at  the  end 
of  six  inches.  Probably  the  deceleration  of  friction  at  the  begin- 
ning would  be  considerably  greater  but  for  the  fact  that  the  outer 
jet  contracts  very  much  as  it  leaves  the  nozzle  and  so  hardly 
touches  the  walls  for  a  certain  distance  from  that  point.  This  can 
not  be  shown  by  the  Pitot  tube  because  of  its  imperfect  action  near 
the  periphery.   See  also  page  10. 

Meanwhile  the  effect  of  the  drag  of  the  outer  wa- 
ter is  propagated  toward  the  center  of  the  driving  stream.  The  ra- 
pid portion  of  this  grows  more  and  more  slender  to  two  inches  from 
the  nozzles.  Here  the  center  continues  to  keep  the  velocity  with 
which  it  left  its  nozzle,  86  ft.  per  second.  From  this  point  onward 
the  slower  water  decelerates  it  until  the  central  speed  becomes  65 
ft.  per  second  at  six  inches. 

There  is  an  irregularity  to  be  noticed  in  all  the 

later  curves  -  that  the  speed  is  greater  above  the  axis  than  at  cor- 
responding points  below  it.  Possibly  this  is  due  to  some  small  ob- 
struction lodfred  in  the  lower  nart  of  the  annular  riozzla  after  one 


30   xiiiti't:    ; 
I  beeqa  arrlai^     ts; 


.0*3 


,-.      ;-    r; 


3 


ifj  tB 


saeioeb  ot   nses 


aqf    .* 
aesit   rrerlt 

n  r*^  f*  f^ 


!  e;i  J  \cf  swarfs   ecf   io:i 
o   608      .Ysarf.-V.J:-*:; 


tfstriw 


Loss     coefficients     begun  -   Inner     nozzle 

or  two  of  the  traverses  had  "been  made.    I   did  not  notice  it  at   the  time 
and  after  the  curves  were  drawn  did  not   have  an  opportunity  of  making 
any  of  the  runs  again. 

LOSSES      IN     PARTS      OF     JET     PUMP 

A  considerable  part   of  the  work  consisted  in  testing 
the   inner  and  outer  nozzles,    mixing  chambers,   and  diffuser  to  find 
their   loss  coefficients.      In  general  this  coefficient,    £  ,    is  defined 
by:   £  v^/feg  =  lost   head(in  feet   of  water)    in  the  part   considered.    It 
is  assumed  that    ^    is  a  constant   for  any  piece  of  apparatus  under 

varying  conditions   of  velocity.      I  found  in  all  cases  that   experi- 

oz   r  ferine  f 

mental  results  for  each  part,  when  plotted  against  v  gave  no  sig- 
nificant trend  either  way,  which  shows  that  the  exponent  2  in  the 
expression  J  v^/2g  is  correct  within  the  limits  of  my  work. 


I   supposed  that  there  was  no  contraction  of  the 

inner   jet  and  made  a  series   of  the   ordinary  tests  to  determine  its 
coefficient,  using'  various  pressures  behind  the  nozzle.    The  water 
issuing  at   each  pressure  was  weighed  for  a  measured  time    .   The 
diameter  of  the  nozzle  is  3/8",    giving  an  area  =  .000768  sq.   ft. 
The  velocity,    v^    ,    is  computed  as  Q/a. 

he          t         Lbs.    CuPt  CuPt       (L  v1  vjf  1  +  i  J 

Wt.  Meter  J  Bg 

185.7    180     1400     22.4  22.5    .0711  92.6  133.1  1.395  .395 

161.5  242     1400     22.4  22.6    .0662  86.2  115.2  1.403  .403 

90.7   317     1400     22.4  22.6    .0506  65.9  67.5  1.345  .345 

35.0  459     1500     24.0  24.1    .0314  40.9  26.0  1.345  .345 

The  impossible  magnitude   of  the    £    thus  obtained 
proves  that  the  jet  must  contract.      I  made  two  other  tests     using 

the  Pitot  tube  to  determine  the  velocity  of  the  water  in  every  part 
of  the  stream,    measuring  the  Pitot  pressure  once  with  a  mercury 


ffl 

ianoo  tfrow  &&t  Jo  JTJ 


e  9iJ*  rtl   ( 

/  et  -i,  lo  9  cat  ( 

T^s   tsriJ'   sseso  IIj5  rf'r 
on  ovs£  v  t8niB3B  I>e 

nl  S  tneriO'-fxs  ecltf-  Jjsrf 
.  ^i  TO   s  *  cjn.t 


lo 


oj-  ata 


erf 


J    ! 


i>rr.s  t©(;  te-t- 

,  ^i'te 
tr  rfose   Jr.  ^.rii/aa 

o^t  erft  l-.t    i 
v    ,  t  ' 


Inner  nozzle  -  Analysis  for  nozzle  coefficient 

column  and  the  other  time  with  a  pressure  gauge.  As  shown  on  page  6 
the  velocity  v  =  12.07  ^  .  Similarly  v  =  .99  J2gx  13.6  hmA2 
=  84.55f  1  ,  where  h  indicates  the  inches  of  me-rcury  -  of  course 


9 


corrected  for  water  column. 

In  the  appended  fi- 

gure let     v     be  the  component   of  the 

x  or        h.  T       •      Y$ 

velocity  of  the  stream  parallel  to 

the  axis  of  the  nozzle  at  a  point 

distant  R  feet  from  it.      Let   dR     re- 

present  the  thickness  of  a  differential 

hollow  cylinder  of  water  of  radius  R 

and  length     v.      The  weight   of  the  water     =  2-rrR  dR  v  y*  ,   where 

y*    is  the     number   of  pounds  per  cubic  foot.      The  integral  of  this 

from  R  =  0     to  R  =  the  outer  radius  of  the   jet  would  be  the  weight 

of  water  leaving  the  nozzle   in  one  second. 

The  kinetic   energy  of  the  differential  cylinder  = 


. 

weight   •   v2/3g     =  ~TMf    R  dR  v5    .     The  total  energy  of  the  water  lea- 

O  " 

ving  the  nozzle  in  one  second  is  the  integral  of  this   from  center  to 
circumference.    If  we  measure  the  variable   radius  in  inches    (  =r), 


the  expression  becomes 


j| 


Now  let  x  =  r2;  thgn  dx  = 


r-dr-2.   Substituting:  Ft.  Lbs.  per  second  of  jet  = 


TT 


The  integral  can  be  evaluated  by  plotting     v5  against 
x    (=  r2).   The  curves  will  be  found  on  curve  sheet  No. 4       and  a  tabu- 
lation of  most   of  the  data  and  computation  is   on  page  10. 

\  cai*      .  6  *  -  ;  ia 

For  the  first  of  the  runs  the  mercury  column  was 

used.  Pressure  pQ  =  23.0  #/D"  }  QQ  =  .0399;  Q8Aj  =  52.0  ft.  per  sec. 
For  velocity  head,  aQ  =  .0104  Oft.  (l  1/4  "  pipe  at  pressure  gauge). 
Hence  ve  =  3.84  and  velocity  head  =  .23  ft.   Pressure  head  =  53.1  ft. 


—    "  **  C 


r 


R 

^JL 


,, 


- 

leJ'WW    -iO'-l    ijy;?' 


erf* 


o  -^afifio-iiaoo  e.".f^  90*     v     t&i   OTW^ 

•  '•  T   "  8      t  :  i  j"     tO     l£  S1 1  CO  j   r3  '•. 


test 


"io  -istBW  lo  Tefcai£\'o.  v?orlorf 
trfiev?  »rfT      .-/     rf^nel 


.tool  oMi/c    7»q  ebmroii  lo   T&C 


ow  *&!;  orfJ1  lo  etfbjsi  teforo  ©rft  «  H  o^     0  «  H  MO-I 

.Ixiooes  Gfto  nt 
s^^ib  srU  lo  \sT«nd  oiJeniat  •iiT 


Jel 


rlt  &i   i>flooe 


efft 
|x 


i   alsad»  t 


j* 


SV 


•  0 


Ji  .8-ifc- 

.  ( 


vx«  01^.3 


eti*  lo  t 


o.ss 


-  10 

Pitot     tube     traverses     of     inner     nozzle 

The  energy  behind  the  nozzle,    then,    =  .0599   •    62.4   •    53.3  =  132.6 
foot   Ibs.  per  second. 

For  the  second  run'.   h_  =  91.  4j   Q_  =  .0523;   VQ  = 

V  V?  C- 

5.03  and  velocity  head  =  .39;    energy  behind  nozzle  =  300.0  ft.    Ibs  /sec. 


First      run 


Second     run 


r 

x  or 
r2 

* 

V 

v^ 

r    x  or    ?„     v     v^ 
r2     *P 

.190 

.0361 

15.  B 

33.5 

37  ,  500 

.190   .0361   21.6   56.0   176,000 

.185 

.0342 

33.5 

48.9 

117,000 

.185   .0342   34.9   71.2   361,000 

.180 

.0324 

43.9 

56.0 

176,000 

.180   .0324   38.2   74.5  415,000 

.170 

.0289 

47.0 

57.9 

194,000 

.170   .0289   38.5   75.0  420,000 

.150 

.0225 

47.2 

58.0 

196,000 

.160   .0256   39.5   75.9  435,000 

.120 

.0144 

47.4 

58.2 

197,000 

.120   .0144   39.5   75.9  435,000 

.070 

.0049 

47.6 

58.3 

198,000 

.020   .0004   39.5   75.9   435,000 

.020 

.0004 

47.2 

58.0 

196,000 

.080   .0064   39.5   75.9  435,000 

.030 

.0009 

47.1 

58.0 

195,000 

.180   .0324   39.1   75.5  430,000 

.060 

.0056 

46.8 

57.8 

192,000 

.185   .0342   35.4   71.7  370,000 

.080 

.0064 

46.8 

57.8 

192  ,  000 

.190   .0361   24.4   59.5  211,000 

.130 

.0169 

46.9 

57.9 

194,000 

.160 

.0256 

46.5 

57.6 

191,000 

.180 

.0324 

46.1 

57.4 

190,000 

Second  run:  area  =  151.4 

.185 

.0342 

45.1 

56.7 

182,000 

D  cm  =  15,140  units;  average 

.190 

.0361 

24.9 

42.1 

75,000 

ordinate  =  mean  v^  =  430,000 

First  run:    area  =  67.28  D  cm  =  6,728  units;   average 
ordinate  =  mean  v3  =  191,100. 

Inserttng  the  area  of  the  curves   in  the  expression 

for  kinetic   energy  on  page  9     gives  142.3     and     320.0  ft.    Ibs  per   sec 
respectively,   values  in  excess   of  the  total  energy  behind  the  nozzle. 
This  is,    of  course,    absurd.      The  trouble  is  due  to  the  fact  that  the 
jet  really  contracts  but  the  Pitot  tube  erroneously  indicates  a  con- 
siderable velocity  up  to  and  beyond  the  point  where  its   center  is   op- 
posite the  edge   of  the  nozzle    (r  =  3A6   "  =  .1875)   as   shown  in  the 
tables  above.   This   is  because  the  water  received  when  the  tube  is 
partly  in  the  air  makes  a  pressure  within  the  apparatus. 

To  avoid  the  difficulty  I   have  taken     v.  =  the 

J 


.A         ~-         A      .* 

J  •         '     a-1*      t*  *  * 

•I  0.00?;  =  alsson  L 


J 

10    X  T 


a . is          o . 


- 


O.V 


0.      0?I. 
0.      031, 


00 


7 


noiaaeiqxa  erfd"  rri   a 


e.ft   tad* 


•rs 


- 


OXtI9I  = 

v  dl 


:  =»  QJ 


ao 


qo   Bt 


cr>;  Y 7  ir> oi ov  e,i.' 

erft  eft       . 

_ 


Contracted     jet      from     inner     nozzle 

cube  root  of  the  average  ordinate  of  the  curve,    considering  it   the 
"effective     velocity"     in  analogy  to  the  use   of  the  word  effective  in 
electrical  calculations.   This  value  is  subject  to  some   error  in  that 

the  curve  area,    taken  for  the  full  radius   of  the  nozzle,    is  wider 
'•:>.   '«?    .   Tfce       C3i    '.•-?.    :t   tta  fcouMfe?1«s    of   the    outet    •  or. •:•  .1  «s  a;-« 
than  it   should  be,    and  the  diminishing  velocity  near  the  periphery 

is  too  large.   The  result  is  that  the  area  of  the  curve  is  considerably 

too  large,   accounting  for  the  tobsurd  result   on  page  10,   but  the  ab- 

It  wa.8          n.  jv.lt   to  Ust^rr^l  n<?  *b«  widtr    ''o  us?.  Is  «-* 
scissal  distance  divided  into  this  area  to  obtain  the  mean  ordinate 

is  also  in  excess,    tending  to  bring  the  mean  ordinate  back  toward  the 

correct  value. 

0 

As  a  check  I  plotted  the  velocity  against  r*  for 

these  two  runs  and  found  the  average  velocity  in  each  case  exactly 

identical  with  the  effective  value.     This   shows  that  with  so  nearly 

finally   tor,.-.   •;-.  «  4:5.5  ae  th«  srt.rage.    ••,-•  '  .-„-,    ;et,fi    >»-o 

uniform  speed  across  the  jet  as  is  usually  given  with  nozzles  it   is 

unnecessary  to  take  the  trouble  to  find  the  effective  velocity. 

The  values   of  v^   as  found  were  57.6  and  75.5  feet 

J 
per  second  respectively  for  the  two  runs,   giving     51.5  and  38.5  feet 

as  the  velocity  heads.  Dividing   into     53.3  and  91.8    (  the  total  -  pres- 
sure and  velocity  -  heads  behind  the  nozzle)   ,    gives  1.035  and  1.037 
as  1  +  ^    in  each  case. 

Another  run,    not  recorded  above  and  not  worked  throu& 
with  the  v^/r2  plot, gave     ^   =  .045.  Giving  greater  weight   to  the   first 

two,    I  take  the  average  value  of    J j   =  .037 

^  ' 
Let  a   .   =  the  contracted  area  of  the   jet,    defined 

"by  QJ  Aj .  The  ratio     aoj /aj      =    °^j    *    the  coefficient    of  contraction, 
where  a^        ^B  the  nozzie  area.   with  this   nozzle  the  three  runs  give 
.000693,    .000693,    and   .000692   =  aOi    .    Hence   CX^=  693/768  =   .90S. 


el  tvtcug  «ff*  lo 
-cfs  edf  *wo'   tOI  e^ecj  no   ^ 

e-  t-.i  •  j 


at 


- 


elf?'1-   . 

G.I 


Friction     and     contraction     coefficients,    outer     nozzle 

To  determine   the  coefficients  of  the  annular  nozzle 

I  made   one  traverse  with  the   Pitot  tube,    measuring  quantity  and  pres- 
spres  as  before,    except  that   instead  of  weighing  the  water  I  sent   it 
into  a  measuring   tank.     The  v-^/r2  curve  will  be  found  on  curve  sheet 
No.    5   .   The     positions  of  the  boundaries   of  the  outer  nozzle  are 

shown  there,   and   it  may  be  seen  that  the   stream  is  very  much  contrac- 

v  ?,o  -vTJ  vJrical  "l  v~-   r*n'/  definite  length  A- 

ted  and  converges   into  the  space  supposed  to  be  occupied  by  the  cen- 

tral  jet.   It  was  difficult   to  determine  the  width  to  use  in  getting 

the  area  and  mean  ordinate,   but     by  several  applications  of  the   cut 

\a  ittp®:U<d  at    i'i.'i   r  £'}"  *^lJi  friction,    li^ 

and  try  method  I   secured  a  fair  approximation  to  a  satisfactory  value. 

The  trials  were  made  by  estimating  the  width,   measuring  the  curve 

area  and  computing  the  average  v,   multiplying  by  the  annular  area 
'•tixlRi      •-itabor*   ir  Baric?.  ",o  the  aosftlee  ami  di 

corresponding  to  the  width  selected,    and  comparing  with  the  measured 

Qs.      I  finally  took  vr  =  43.2  as  the  best  average,   using  both  the 

v^/r2  curve  and  a     v'r2  curve    (the  latter  not  preserved),   i^is  gives 
•to  att          <  A  \ir.i.  e-.'-.i  aorofcs  the  v;ros«  r--'o1 

the  velocity  head  =  29.0.   The  pressure  head  back  of  the  nozzle  =  29.8 

feet    (12.9  #/!*   on  gauge),    and  the  velocity  head  was   neglected,    jjence 
1  +  "£  =  1.027.   Since  an  inaccuracy  of  even   .  1#  in  the   gauge  would 

'-    •  '     "'"  >' 

change  the  value  of  jr  thus  derived  to  .018  or  .035  ,  the  result  is 
not  very  reliable.   It  is  unimportant,  however,  for  as  will  be  shown 

later  (page  18  )  the  loss  in  this  nozzle  is  almost  zero  compared  with 

;,..;>      >^ci  to  tha  emois  of  th*  d  if  fax 
the  other  losses  in  the  jet  pump. 

„  »   ..  j    4  —       T-  ?  f  i  -  ft,  a     •*•>••    *•  Htf> 

'     i       >  *  .  -  ^       .  .  .    \>  G         •-  *  i 

Qa  in  this   test  was   .04461.   Baking  vr  =43.2  we 

find  aor  =  .04461/43.2  =  .001033  Dft.      The  nozzle  area,    ar,   =  .00136; 
hence  CXr  =  1033  A3SO  =  ,76    .   This   is  much  more  accurate  than  the 


value,    for  it   does  not  depend  at  all  upon  the  pressure  measurement. 

Of   course,   aor  indicates  the  area  of  the  contracted  stream  leaving 

:-    u    ;.<*b!3<  of  >    t*»   o* 
the  annular  nozzle     =  Qs    /vr    . 


erit/o  no  bauclt  »cf  XI  r* 

©Isson  iPtifo  erftf  lo   s 


;  Lt    V1-.  V    FiX    I.'..  Sr1. 

\cf  Jbeiqjjfooo  ecf  o^  i)ea 
at  ©e*f  ot  ifj-fjiv.-  eift  e 


fi  o 


ijevrreeeiq  Jon 


is    ed"  II 


.    •&  8X0. 

j'r.eVewoil    t 


.  a  . 


I   Lcdt&tf. 


l*  of 

Jtoo.1 


en'T 


s  fen^  8Vii/r 


I  fc 


e.T;l) 


.730.1 
lo 


-*•  I 


0, 


-j.  = 


Method     of     getting     mixing     chamber     coefficient 

Since  a  number  of  mixing  chambers   of  different 

lengths  are  used  with  this   jet  pump,   a  more  convenient   form  for  the 
friction  coefficient   is    X   instead  of     £    .   The  symbol   is  defined  by: 
lost   head   (in  feet   of  water)   =   Xl/d  •   v2/2g  ,   where  1/d  is  the  ra- 
tio of  the   length  considered  to  the  diameter  -  of  course  ajbplying 
only  to  cylindrical  bore.     For  any  definite  length     £     =      Xl/d.    For 


a  uniform  flow  of  water  between  the  points  1  and,  3  of  a  cylindrical 
?h  £ave  lat^n';  results,    tha  ralu^fs   fc  ;o,-      \ 

tube,    the  speed  of  the  water  being  constant  throughout  the  area  ex- 

cept  as  impeded  at   the  periphery  by  skin  friction,    h1  +  v2/feg  =     hg 
+  v2/feg  +   Xl/d  •   v2/feg  ;    hence     Xl/d  =   (hx  -  hs)  +  v2/2g   . 

The  method  of  testing  was   to  connect   several  of  the 
mixing  chambers   in  series  between  the  nozzles  and  dlffuser  and  send 
\vater  through  from  both  orifices  at   once  under  equal  pressures.    To 
escape  the  complications  at   the  contracted  jet  and  to  allow  the  water 
to  achieve  a  uniform  speed  across  the  cross  section,    the  measurements 
were     always  made  at   least   six   or  eight    inches  from  the  nozzle  plane. 

j1 

Water  and  mercury  manometers  were  used  to  measure  the  drop  in  head 
across  all  possible  different    combinations   of  mixing  chambers,    and 
the  water  was  weighed  and  the  time  measured  for  each  run.   One  side 
of  the  manometer  was  always  connected  to  the  throat   of   the  diffuser 
and  the   other  side  connected  to  the  ends   of  the  different   chambers, 
a  small  brass  tube  being   inserted  in  orifices  in  ithe  flanges  which 
communicated  with  the  interior.   Because   the  aperture   in  the  throat 
was   located  about   3/8  "  from  the  end  of   the   last   chamber  it  was  ne- 
cessary to  add  this  length   (which  is  that    of  the  cylindrical  portion 
of  the   diffuser)   to  the  length  of  mixing  tube  measured,     a^  =.OOS13G  '. 

Following   is  a  table   of  a  few  of  the  tefcts: 


io     ISTO;!    Jneinevnoc.  etoi 
&ftj-leJb  ei  locfsrta  erfT   . 


erf* 


,i>\lX 


erf?  lo 

Itnee  i>«jb  TOBirll  rb  :  :^  eelsson 

OT     .  86-  ti/t.8©10[ 

tre.ti-w  feiU  7?oXljs  ot  Lrr>5  t&t  i'&^o 
£drr&raeiuaB«r.  ^;<j-    jfloitoeB  ssoio 
.artfilq  elssorr  erff  MOT!  setioat 
t*.er(  at 


fetoilleoo  nol 

*»el  nr)    t,;;.vr' 

rfjTjrvel  eri*   ? 

jeoiTt>atlYs  o* 

lo  wo  II 
to  i.eeq 
*>?  babeqrui   BJS    J 

•   £\£,<    -f  £,^S 

ni   eiedafiao     rt 


20 


lo   liiO'i  i*  erfj   o* 


i.'f'W    88">.alBr"l    ©rT* 


e   'i  J" 


•i  - 


•  ^ 

. 


Mixing  chamber  and  diffuser  coefficients 


14 


Water 
Lbs. 
1100 

t 
sees. 
700 

1500 

483 

1500 

366 

Length 

(hj-ho  ) 

Al/d 

X 

inches 

Ft.  Water 

8.75 

.708 

.326 

.0233 

17.25 

1.383 

.637 

.0231 

2.75 

1.033 

.122 

.0277 

4.75 

1.475 

.174 

.0230 

2.75 

1.575 

.107 

.0243 

4.75 

2.520 

.171 

.0225 

8,75 

4.100 

.278 

.0199 

17.35 

7.830 

.535 

.0193 

Omitting  tests  with  very  short  lengths  (under  two 

inches),  which  gave  inconsistent  results,  the  values  found  for   \ 
are  shown  in  the  following  table.  The  table  on  the  right  gives  values 
of  ^  for  all  the  different  mixing  chambers,  computed  from  the  mean 
X  =  .0243  by  £  per  inch  length  =  X  +  5/8  =  .0389. 

.--"..  ••'         •<      •••   >-  —    -v   .*.    •.         fi4t~        "*•    '• '  iL        ""  *       ""  tw< '   '  *  "*  •    '    i7 

. ••:•      L  .  a  v*  v     IM 


Length  velocities  Mean 

inches  used  X 

3.75  23  -  31  .0260 

4  36  13  -   20  -  26  .0234 

I!75  12  -   23  -   31  .0236 

6.25  13-20  .0262 

8.75  12  -   31  -  35  .0240 

17.25  12  -   31  -   35  .0226 


Final  Average    .0343 


Mixing 
Chamber 

0 

1   in. 
13/8 

2 
2   1/2 

3 

4 

5 

6 

^   depended  upon  the   speed 


Cylindrical 
length 

.5  in. 
1.5 
1.875 
2.5 
3.0 
3.5 
4.5 
5.5 
6.6 


,020 

,058 
073 
097 

,117 
136 
175 

,214 
253 


In  order  to  find  whether 
of  the  water  I  plotted  all  the  values  against  v,  and  found  the  curve, 

r  .-»••*-      >*  *  '   f 

though  exceedingly  irregular,  roughly  parallel  to  the  axis  cf  v. 

To  find  the  coefficient  of  the  diffuser, water  was 

run  through  it  at  measured  rates  and  the  difference  in  pressure  be- 
tween the  two  ends  read  on  a  mercury  column.  The  water  came  through 
both  nozzles  at  the  same  pressure  and  several  mixing  chambers  were 
inserted  to  give  it  time  to  get  over  the  effects  of  contraction  and 
impact.  The  loss  in  head  is  refferred  to  the  higher  velocity,  vt  , 
and  =  bdv|/2g  =  v|/3g  -  v|/3g  -  (hf  -  ht).  Following  is  a  table 


, 


. 


f..L 

sol     bnwcl 


;«i    i.! 


rfrrrfi?:'   t(8«rfo*tl 

. 

'x   f-rlj"  I  IB  to  1     ^      lo 
Toq[  Si  30. 


iel«co 


>.:!&    ,v 


s   r 


• 


^  w 


sr,  it 


•      r  V  J  .     V 


ti  * 


Analysis  of  friction  in  mixing  chamber 

showing  the  values  obtained  in  eight  different  runs: 
vt      13.0   30.3   21.8   26.0   39.7    30.7   30.7   33.7 
3d     ..138    .120   .135    .113    .111    .110   .110    .116 

The  average  of  all  these  values  is  ld  =  .119  or  .12 
Two  other  runs  under  similar  conditions  gave  answers  so  widely  dif- 
feront  as  to  show  error  in  measurement  or  irregular  action  and  their 
results  were  thrown  out. 

ANALYSIS  OF  FRICTION  IN  MIXING  CHAMBER 
It  is  customary  to  express  the  head  lost  due  to 

friction  in  the  mixing  chamber  as  v£/feg  *  £  m  ,  where  vt  is  the  aver- 
age value  of  the  speed  of  the  water  at  the  throat  of  the  diffuser, 

'••'i        , t  ir.  the  tn.t.viri^,         that 
of  Qf  /at  .  This  is  considerably  in  excess  of  the  true  loss  of  head, 

for  the  rubbing  velocity  is  variable  through  the  tube,  never  becoming 
so  great  as  v^  and  approaching  it  only  near  the  end.  It  is  theoreti- 
cally vr  at  the  plane  of  the  nozzles,  assuming  no  contraction.  Hence 
a  ,nearer  approach  to  exactness  would  be  to  substitute  for  v^  in  the 
expression  above  an  average  velocity  =  (vr  -fv^)/2  .  This  gives  head 
lost  =  ~£  ffi-  (vr  +  vt)^/feg  .   It  should  be  noted  in  this  connection 
that  any  measurement  of  ]>  such  as  recorded  on  pages  13  and  14  must 
be  made  with  constant  rubbing  velocity.  The  term  'rubbing  velocity' 
as  used  here  refers  not  to  the  actual  speed  of  the  water  particles 
in  contact  with  the  wall  of  the  tube,  but  to  the  velocity  of  the  ma- 
jor part  of  the  water  near  it  -  a  value  corresponding  to  the  velocity 
obtained  in  the  tests  mentioned  by  dividing  Q  by  a^ . 

Following  is  the  derivation  of  an  expression  for 

the  loss  of  head  here,  which  is  perhaps  more  accurate,  at  least  theo- 
retically, than  those  mentioned  above.  No  account  is  taken  of  the 


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16 

Comparison     of     mixing     chamber     loss     formulas 

contraction  of  the  jets  and  it  is  assumed  that  the  rubbing  velocity 
varies  uniformly  from  end  to  end  of  the  mixing  chamber,  which  seems 
to  be  in  substantial  accord  with  the  facts. 

Referring  to  Fig.   2     on     Sketch  Plate  No.   1,    in  the 
differential  distance     dl     there  is  a  loss   of  head  =    X'dl/d  •    v2/2g 
where  v  represents  the  rubbing  velocity  and  =  vr  +   (v^  -  vr)    •   lAm. 
The   total  head  lost   in  the  tube  is  the   integral  of  the  differential 


f~m 

loss  between  1=  0  and  1  =  1,    or      X/fedg    •  I        v^  dl  +  2vr(v-t-vr)  Am' 

/o 

dl  +   (vt  -  vr)2    A£  •   12  dl     =        X/2dg  f  vr2  lm  +  2vr(vt  -  vr)Am  • 


lg/3  +   (vt  -  vr)2  A|  •   Ig/s     =    f  m/feg   •  (vj  +  vrvt  +  vf  )       since     " 
X  Im/d  "  $»•        This  is  the  head  lost   in  the  mixing   chamber,   that 

is,    the     amount  by  which  the  water  reaches  the  throat  robbed  of  the 

v  >   >?  i 
pressure  it  would  have  had  if  there  were  no  friction.   Hence  the  ener- 

gy at   that  point    is   less  than     the  no-friction  value  by     the  quantity: 

Qf  ^  '  im/6&   *    (vr     +     vrvt     +     vt   )     »   which  is  the   loss  of  energy 
per   second  through  the  tube. 

To  compare  the  result   thus   obtained  with  the   other 
formulas  mentioned  previously,  I  have     computed  the  loss  in  each  of 
the  three  ways  in  each  of  five  runs  made  with  the  six   inch  mixing 
chamber.   The  data  and  computation  follow: 
Run  Qf  vr         vt  Qf     v^/2g         Qf      (vr+vt)2/8g     Last  Way 


1  .111    35.0  52.1            73.8  51.5          52.3 

2  .1052   31.2  49.4           63.6  41.9          42.6 
.0976   25.9   45.8           50.2  30.7          31.6 

4  .0889   17.2  42.2            39.2  19.2          20.4 

5  .0769    4.6  36.1           24.5  7.8           9.3 

It  is  seen  that  the  losses  "last  way"  and  using 

the  average  velocity  are  in  close  agreement  and  much  lower  than 
the  value  obtained  in  the  usual  wav. 


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Professor     Hesse's      expression     for     impact      loss 

IMPACT      LOSSES 

All  the  friction  losses   in  the   jet  pump  are  not 
enough  to  account   for  its  low  efficiency.   (She  additional  loss  is 
considered  to  be  due  to  impact  and  eddying  in  the  mixing  chamber, 
and     in  the  analysis  as  developed  by  Professor  Hesse  it  has  been 
expressed  by  the   same  formula  as  that  used  for  the   loss  due  to 
sudden  enlargement   in  pipe  section.     Both  the  suction  water  and  that 
entering  through  the  central  nozzle  are  considered  to  suffer  loss 
of  energy  in  this  way,    making   the  total  diminution  of  energy  = 
Qe)f  (v.j-  vt)s/2g+ Qsv>(vt-  vr)2/3g  ,   as   for  sudden  enlargement. 

In  order  to  test  the  reliability  of  this  expres- 
sion and  at  the   same  time  secure  as  thorough  a  check  as  possible 
on     all  the  work  described  in  this  thesis,    I  have     computed  the 
entire  losses  for  the  series   of  five  runs  made  with  the  six  inch 
chamber  with  70#/D  "  pressure   on  the  inner  nozzle.   The  data  will 
be   found  on  page  6.     Below  are   the  work  and  results .    It  will  be   seen 
that   the  sum  of  the  computed  losses  of  friction,    impact  ancl  eddying 
is  almost  exactly  equal  to  the  difference  between  output  and  input. 
Velocity  heads  are  allowed  for  for  both  the  delivery  water  and  that 
entering  the  central  nozzle,   and  the  work  has  been  checked  over  to 
insure  accuracy  in  the  mathematics. 

See  the  following  page   for  the  tabulation: 


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Input,      output, 
Run     Time       tQ 

and     losses 

A               3        O 

computed. 

Energy     balance. 
tQ8         Qs       Qs/*or 

sees.                                    ^vi)" 

V 

|/2g 

(vr) 

1          73 

5.4 

.0750 

108. 

•3 

31.4 

2.6 

.0361 

35.0 

3          76 

5.5+ 

.0730 

105. 

s 

39.0 

3.5- 

.0322 

31.2 

3          82 

5.8 

.0707 

102. 

0 

26.3 

2.2 

.0263 

25.9 

4          90 

6.4 

.0711 

102. 

6 

36.8 

1.6 

.0178 

17.2 

5        104 

7.5 

.0722 

104. 

1 

28.0 

0.5 

.0048 

4.6 

Rttn       tQf 

•&  Qf 

Qf/at 

I 

Q 

v 

S 

d 

v3+vr 

vt+v2 

%fA( 

(vt) 

V 

\fe 

8 

1         8. 

0 

.1110 

52.1 

35. 

0 

5, 

763 

2          8. 

0 

.1052 

49.4 

29. 

3 

4, 

954 

i 

3          8. 

0 

.0976 

45.8 

23. 

8 

3, 

956 

j 

4          8. 

0 

.0889 

42.2 

18. 

4 

2, 

803 

< 

5          8. 

0 

.0769 

36.1 

11. 

7 

1, 

483 

1.3 
.9 
.5 
.2 
.003 


53.3 
42.4 
31.6 
20.4 
9.3 


Run 


1 
3 
3 

4 
5 


228 
213 
217 
252 
334 


Run 

1 
3 
3 

4 
5 


Output 


10.2            21.5 

50.1 

112.3 

113.3 

10.3            24.4 

56.8 

114.1 

105.5 

10.3            38.2 

65.4 

109,5 

96.9 

10.8           31.1 

72.1 

80.1 

90.3 

4.6            34.0 

78.7 

23.6 

83,6 

Input  -  Output 

Sum 

computed  losses 

413 

358 

366 

525 

317 

309 

320 

329 

353 

378 

Input 

526 
480 
427 
400 
377 


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19 

Conclusion 

CONCLUSION 

The  results   of  the  investigation  have  been: 
With  constant   applied  pressure  from  thirty-nine 

to  seventy  pounds  per  square   inch  above  atmosphere,   the  efficiency 
of  this   jet  pump   reaches  a  maximum  when  the  delivery  pressure  is 
about     thirty-four  par-cent    of  that  applied,   the     suction  pressure 
being  atmospheric    .     Comparing  mixing  chambers  shows  that  under 
these  conditions  the  greatest   efficiency  -  about  thirty-two  per-cent, 
is  secured  by  using  the  three   inch  chamber.   However,   any  length  from 
one  and  three-eights  inches  to  four  gives  almost  as  good  operation. 
All   lengths  outside  of  these  show  much  lower  efficiency. 

The  Pitot   tube  traverses  show  that,   with  fifty  and 

nine  pounds  respectively  behind  the  inner  and  outer  nozzles  the  jets 
mingle  in  a  distance  of  six  inches  so  that  the  highest   velocity  in  the 
center   is  less  than  three- halves  that   of  the  slowest  water.  Up  to  this 
point   the  outer  jet   is  continually  accelerated  and  the   inner  one  re- 
tarded. 

The  loss  coefficients   of  the  parts    of  the  pump  are: 
Inner   nozzle,    .037;    outer  nozzle,    .03;      mixing  chamber,    .0389  per 
inch  length;    diffuser  .12.      The  coefficient   of  contraction  of  the  in- 
ner nozzle  =.902     and  of  the   outer  nozzle      .76 

The  expression  derived  by  integration  for  the  fric- 
tion loss   in  the  mixing  chamber  has  been  checked  numerically  on  a 
reasonable  approximation. 

Professor   Hesse's  expression  for  the   less  due  to 

impact  has  been  tested  by  substituting  values  from  five   efficiency 
runs  and  shown  to  a^ree  very  closely  with  the     loss  not   accounted  for 
by  friction.     Incidentally  a  rough  check  was   secured     on  all  the 


meed  evari  nc 
. 


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20 


coefficients  found  and  the  mixing  chamber  formula.  However,  since  im- 
pact represents  over  two-thirds  of  the  total  loss,  the  latter  check 
has  little  importance. 

I  would  suggest  that  a  further  study  of  the  impact 
loss  with  this  apparatus  would  probably  prove  valuable.  The  data 
tabulated  in  this  report  would  furnish  material  for  determining  the 
loss  by  impact  under  conditions  of  considerable  variation,  and  perhaps 
point  the  ^ay  to  the  discovery  of  a  more  accurate  expression  for  this 
very  important  factor  in  jet  pump  operation. 


COl 


8  S 


31 


The     Jet     Punp     Disassembled 


22 


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4* 
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P! 

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+» 

O 

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O 
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23 


Assistant  Measuring  Weight  and  Time  to  Determine 


24 


Traverse  at  Nozzle  with  Pitot  Tube  and  Mercury  Column 


25 


Pitot  Tube  Traverse  at  End  of  Mixing  Chamber 


S6 


CO 


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M 
0) 


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1-1 


27 


Connections  to  Inverted  water  Column  for 
Testing  Mixing  Chamber  Coefficients 


28 


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33 


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NON-CIRCULATING  BOOK 


U.C.  BERKELEY  LIBRARIES 


245594 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


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